Using Dynamic Analysis for Compact Gear Design

This paper presents procedures for designing compact spur gear sets with the objective of minimizing the gear size. The allowable tooth stress and dynamic response are incorporated in the process to obtain a feasible design region. Various dynamic rating factors were investigated and evaluated. The constraints of contact stress limits and involute interference combined with the tooth bending strength provide the main criteria for this investigation. A three-dimensional design space involving the gear size, diametral pitch, and operating speed was developed to illustrate the optimal design of spur gear pairs. The study performed here indicates that as gears operate over a range of speeds, variations in the dynamic response change the required gear size in a trend that parallels the dynamic factor. The dynamic factors are strongly affected by the system natural frequencies. The peak values of the dynamic factor within the operating speed range significantly influence the optimal gear designs. The refined dynamic factor introduced in this study yields more compact designs than AGMA dynamic factors.

Computerized Design, Generation and Simulation of Meshing of a Spiroid Worm-Gear Drive With Double-Crowned Worm

The authors propose methods of computerized design and analysis of a spiroid worm-gear drive with ground worm based on the following considerations: (1) The theoretical thread surface of the hob is generated by a cone surface. (2) The worm surface is crowned in profile and longitudinal directions in comparison with the hob thread surface. (3) The double crowning of the worm enables to localize the bearing contact and obtain a predesigned parabolic function of transmission errors of an assigned level. Computerized design of the worm-gear drive enables to discover and avoid singularities of the generated worm face-gear surface and pointing of teeth. The meshing and contact of the double-crowned worm and the worm face-gear is simulated to determine the influence of misalignment on the shift of bearing contact and transmission errors. Computer program for numerical solution is developed and applied. A numerical example that illustrates the developed theory is provided.

Vibro-Acoustic Studies of Transmission Casing Structures

Automotive transmission casing plates of irregular shape, with complex boundary conditions and non-uniform material properties, are experimentally and computationally studied to acquire a fundamental understanding of their dynamic and acoustic radiation characteristics. A modified flat cover is designed which simplifies the geometry while providing uniform thickness and material properties. Both covers (“real-life” and “laboratory”) are studied with free and bolted boundary conditions. In particular, the free boundary conditions are useful because they eliminate the cover-housing interaction allowing for a more detailed analysis of the cover plate. Finite element models for both covers under the free boundary conditions are developed and refined. Predicted natural frequencies and mode shapes are in excellent agreement with measured modal data. Then the finite element models are coupled with boundary element models to predict acoustic radiation properties. Predictions match well with measured acoustic directivity at resonant frequencies.

Single Flank Test, Structure-Borne Noise Analysis and Digital Imaging of Tooth Contact

The innovative new measuring and testing machine is not only a high-precision measurement for the laboratory, but also a 100% inspection tool for the production environment or for quality control. It is incorrect to currently assume that a production tester can be less precise and should be without advanced measurement and analysis features. Today’s quality standards demand a full-featured production test machine, which brings lab-testing abilities to the shop floor. The laboratory investigation can establish the combination of criteria to be fulfilled by an individual gear set in order to pass acceptance in the vehicle. This can include requirements related to tooth contact, structure-borne noise emission or single flank variations. It is not necessarily evident, beforehand, if criteria for all three test types can be established or are even mandatory. It is quite possible, for instance, that the analysis of vibrations a gear set transmits to the spindle housing of the testing machine does not reveal a correlation with the noise in the vehicle. The noise levels of a “quiet” gear set may well be higher on the testing machine than those of a “loud” gear. In this case, the single flank test or a combination of single flank test and structure-borne noise analysis will provide a criterion for testing. All options and features described are equally important in both laboratory and production use. Specific software and electronic hardware components for single flank testing and structure-borne noise analyses are and commanded by the part program executed in the machine controller. The use of the video equipment on the tester can recognize and evaluate the contact position.

Determination of Principal Curvatures and Contact Ellipse for Profile Crowned Helical Gears

Helical gears with localized bearing contact of tooth surfaces achieved by profile crowning of tooth surfaces are considered. Profile crowning is analyzed through the use of two imaginary rack-cutters with mismatched surfaces. The goal is to determine the dimensions and orientation of the instantaneous contact ellipse from the principle curvatures of the pinion and gear tooth surfaces. A simplified solution to this problem is proposed based on the approach developed for correlation of principal curvatures and directions of generating and generated tooth surfaces. The equations obtained are applied to three cases of profile crowning where the normal profiles of the rack-cutters are: (i) parabolic curves: (ii) circular arcs; and (iii) a combination of a straight line for one of the rack-cutters and a parabolic curve or a circular arc for the mating rack-cutter. The gear drives can be the combination of a pinion generated by a parabolic curve or a circular arc and gear generated by one of three cases mentioned above.

Calculation of Wobble From Lead Inspection Data of Gear Teeth With Modifications

The effect of the reference misalignment including eccentricity and wobble on profile and lead inspection traces is discussed. The relative slopes of the lead traces induced by wobble are used to calculate the magnitude of the wobble. The deviation caused by the wobble is removed from the lead inspection results. This method is theoretically ‘exact’ for spur gears and is approximate for helical gears. Real measurement examples show this method produces a good result with a spur gear and a satisfactory result with a helical gear.

Pitting Life of Ground, Carburized and Hardened Gears With Uncontrolled Heat Treat Distortion

Carburized and hardened gears are generally ground to improve the quality of distorted tooth geometry caused by heat treatment. As long as the distortion is low and predictable, stock removal from teeth is small up to a maximum of 0.005 inch from each flank. This allows minimum tooth surface hardness reduction with no deterioration of these gears. Uncontrolled distortion, on the other hand, may result in an undue amount of stock removal with a significant loss of tooth surface hardness. Lower surface hardness reduces gear life due to tooth pitting. For heavily distorted gears, the pitting life may be reduced as much as 30% after grinding. For a realistic evaluation of the pitting life of ground, carburized gears with uncontrolled distortion, derating factors are established for a number of gear materials.

Design and Stress Analysis of Gears Using the Boundary Element Method

Basic design and stress analysis of gears can be, for the most part, accomplished through the use of the American Gear Manufacturers’ Association (AGMA) criterion or use of a machine design text book such as Norton[1]. Real life questions as to the effect of undercut, misalignment, notches or grooves, and so on are not answered quite so quickly or with reasonable accuracy. The boundary element method (BEM) provides a relatively quick modeling method for assessing stresses and a means to accurately predict crack propagation in components. Lubricated bodies in contact, such as gears, cams and bearings, provide an application for which BEM can be applied. This paper has been written to provide an assessment of the use of BEM to evaluate the effect of undercut on the stresses in a gear, the propagation of a notch in the root of a gear, with and without undercut. Future work will be expanded to include contact analysis using a second gear and three dimensional analysis, possibly providing a means for assessing misalignment of gears and load distribution effects on gears.

Robust Design of Gears

The terms “Robust Design” or sensitivity of a design to variance of design parameters is gaining importance in design of mechanical components and structures. This paper has been written as the result of an introductory investigation to determine the applicability of robust design for a given gear system and development of a model to perform the evaluations. Work has been performed based upon evaluation of a design being performed using AGMA standards.

Profile Modifications for Minimum Static Transmission Error in Cylindrical Gears

The theoretical advantage of conjugate action in involute gears is lost due to the deflection of the teeth under load and due to manufacturing and assembling errors. These factors produce instantaneous variations in the gear ratio commonly referred to as transmission error. The transmission error has been proven to have a strong relationship with the noise emitted by the transmission. In order to reduce the transmission error, the contacting surfaces of the gears are modified to compensate for the deflections and errors. These modifications may be performed in the direction of the profile, the lead or in a more general sense it may be topographical (defined point by point). This paper describes a non-iterative procedure for the calculation of the modifications for minimum transmission error based on a predefined load distribution. The results presented agree with the common practice for spur gears of tip relief in the direction of the profile and crowning in the direction of the lead, but for helical gears the need for a more complicated modification is observed.